A Model-Based Heuristic for the Irregular Strip Packing Problem

Cherri, Luiz Henrique; Carravilla, Maria Antónia; Toledo, Franklina Maria Bragion de

doi:10.1590/0101-7438.2016.036.03.0447

Cited by 16 publications

(10 citation statements)

References 22 publications

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“…The basic NFP-CM-VS model is defined by the objective function (17) and the constraints (18)(19)(20)(21)(22)(23)(24)(25)(26)(27)(28)(29)(30)(31)(32), whilst the full NFP-CM-VS model is defined by the former objective function and the constraints, symmetry breakings, valid inequalities, and variable eliminations in expressions . The objective function (17) together with the constraints (18)(19)(20)(21)(22)(23) fit the definition of the basic NFP-CM model without cuts [25], with the only exception of our two distinguished binary variables and encoding the left and right feasible sub-regions shown in figure 5, whilst the constraints (24-29) encode our new convex decomposition based on vertical slices, which removes all symmetric solutions derived from any relative placement between pieces.…”

Section: The Nfp-cm-vs Modelsmentioning

confidence: 99%

A new mixed-integer programming model for irregular strip packing based on vertical slices with a reproducible survey

Lastra-Díaz¹,

Ortuño²

2022

Preprint

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The irregular strip-packing problem, also known as nesting or marker making, is defined as the automatic computation of a non-overlapping placement of a set of non-convex polygons onto a rectangular strip of fixed width and unbounded length, such that the strip length is minimized. Nesting methods based on heuristics are a mature technology, and currently, the only practical solution to this problem. However, recent performance gains of the Mixed-Integer Programming (MIP) solvers, together with the known limitations of the heuristics methods, have encouraged the exploration of exact optimization models for nesting during the last decade. Despite the research effort, the current family of exact MIP models for nesting cannot efficiently solve both large problem instances and instances containing polygons with complex geometries. In order to improve the efficiency of the current MIP models, this work introduces a new family of continuous MIP models based on a novel formulation of the NoFit-Polygon Covering Model (NFP-CM), called NFP-CM based on Vertical Slices (NFP-CM-VS). Our new family of MIP models is based on a new convex decomposition of the feasible space of relative placements between pieces into vertical slices, together with a new family of valid inequalities, symmetry breakings, and variable eliminations derived from the former convex decomposition. Our experiments show that our new NFP-CM-VS models outperform the current state-of-the-art MIP models. Finally, we provide a detailed reproducibility protocol and dataset based on our Java software library as supplementary material to allow the exact replication of our models, experiments, and results.

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Section: The Nfp-cm-vs Modelsmentioning

confidence: 99%

A new mixed-integer programming model for irregular strip packing based on vertical slices with a reproducible survey

Lastra-Díaz¹,

Ortuño²

2022

Preprint

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“…Another model based on CLP was presented by [11]. The researchers reported constraints aiming to ensure all feasibility requirements to achieve a solution.…”

Section: Approaches To Tackle Irregular Strip Packing Problemsmentioning

confidence: 99%

A Parallel Biased Random-Key Genetic Algorithm with Multiple Populations Applied to Irregular Strip Packing Problems

Júnior

Pinheiro

Coelho

2017

Mathematical Problems in Engineering

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The irregular strip packing problem (ISPP) is a class of cutting and packing problem (C&P) in which a set of items with arbitrary formats must be placed in a container with a variable length. The aim of this work is to minimize the area needed to accommodate the given demand. ISPP is present in various types of industries from manufacturers to exporters (e.g., shipbuilding, clothes, and glass). In this paper, we propose a parallel Biased Random-Key Genetic Algorithm (µ-BRKGA) with multiple populations for the ISPP by applying a collision-free region (CFR) concept as the positioning method, in order to obtain an efficient and fast layout solution. The layout problem for the proposed algorithm is represented by the placement order into the container and the corresponding orientation. In order to evaluate the proposed (µ-BRKGA) algorithm, computational tests using benchmark problems were applied, analyzed, and compared with different approaches.

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“…In this research, we cut the stock into a triangular shape. Cherri et al (2016) explained that in the 3-Phase Matheuristic model, there were 3 phases including a constructive phase which is useful to get an initial solution, an improvement phase to improve the initial solution and a compaction phase to increase the initial solution to best solution. The 3-Phase Matheuristic model has 2 models namely the Dotted Board model that has been described by Gomes and Oliveira (2006) and the Mixed Integer Linear model that has been described by Toledo et al (2013).…”

Section: Introductionmentioning

confidence: 99%

3-Phase Matheuristic Model in Two-Dimensional Cutting Stock Problem of Triangular Shape Items

Bangun¹,

Octarina

Sepriliani³

et al. 2020

sci. technol. indones.

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Cutting Stock Problem (CSP) is a problem of cutting stocks with certain cutting rules. This study used the data of rectangular stocks, which cut into triangular shape items with various order sizes. The Modified Branch and Bound Algorithm (MBBA) was used to determine the optimum cutting pattern then formulated it into the 3-Phase Matheuristic model which consisted of constructive phase, improvement phase, and compaction phase. Based on the results, it showed that the MBBA produces three optimum cutting patterns, which was used six times, eight times, and four times respectively to fulfill the consumer demand. Then the cutting patterns were formulated into the 3-Phase Matheuristic model whereas the optimum solution was the minimum trim loss for the first, second and third patterns.

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A Model-Based Heuristic for the Irregular Strip Packing Problem

Cited by 16 publications

References 22 publications

A new mixed-integer programming model for irregular strip packing based on vertical slices with a reproducible survey

A new mixed-integer programming model for irregular strip packing based on vertical slices with a reproducible survey

A Parallel Biased Random-Key Genetic Algorithm with Multiple Populations Applied to Irregular Strip Packing Problems

3-Phase Matheuristic Model in Two-Dimensional Cutting Stock Problem of Triangular Shape Items

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